Problem: Solve for $x$ and $y$ using elimination. ${-3x-y = -16}$ ${2x+y = 13}$
We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-y$ and $y$ cancel out. $-x = -3$ $\dfrac{-x}{{-1}} = \dfrac{-3}{{-1}}$ ${x = 3}$ Now that you know ${x = 3}$ , plug it back into $\thinspace {-3x-y = -16}\thinspace$ to find $y$ ${-3}{(3)}{ - y = -16}$ $-9-y = -16$ $-9{+9} - y = -16{+9}$ $-y = -7$ $\dfrac{-y}{{-1}} = \dfrac{-7}{{-1}}$ ${y = 7}$ You can also plug ${x = 3}$ into $\thinspace {2x+y = 13}\thinspace$ and get the same answer for $y$ : ${2}{(3)}{ + y = 13}$ ${y = 7}$